A thorough study of the performance of delta-coupled-cluster (ΔCC) methods for calculations of core-ionization energies for elements of the first long row of the periodic table is reported. Inspired by the core-valence separation (CVS) scheme in response theories, a simple CVS scheme of excluding the vacant core orbital from the CC treatment has been adopted to solve the convergence problem of the CC equations for core-ionized states. Dynamic correlation effects have been shown to make important contributions to the computed core-ionization energies, especially to chemical shifts of these quantities. The maximum absolute error (MaxAE) and standard deviation (SD) of delta-Hartree-Fock results for chemical shifts of core-ionization energies with respect to the corresponding experimental values amount to more than 1.7 and 0.6 eV, respectively. In contrast, the inclusion of electron correlation in ΔCC singles and doubles augmented with a noniterative triples correction [ΔCCSD(T)] method significantly reduces the corresponding deviations to around 0.3 and 0.1 eV. With the consideration of basis set effects and the corrections to the CVS approximation, ΔCCSD(T) has been shown to provide highly accurate results for absolute values of core-ionization energies, with a MaxAE of 0.22 eV and SD of 0.13 eV. To further demonstrate the usefulness of ΔCCSD(T), calculations of carbon K-edge ionization energies of ethyl trifluoroacetate, a molecule of significant interest to the study of X-ray spectroscopy and dynamics, are reported.